## 8.7 Conclusions & Summary

#### General: Section I: Foundations of Live Data Stream Science

Section I: starts with a brief discussion of the foundations Data Stream Science. Section IA: Reviews the Root & Seed Equations. It is discovered that they determine Laws not Mechanisms. Laws determine structure. Mechanisms determine process. Section IB: Discusses another difference between Live & Dead Data Streams, their functions. The Functions of Dead Data Streams determine the exact route. The functions are everything. The Functions of Live Data Streams just determines the possible routes. The Data is everything.

#### Section II: A Study in Unraveling: A & B

IIA: Discusses the number of elements in each Unraveling and also derives a general equation to determine the general number of terms in an expression that has been raveled Q times. The number of terms expands so rapidly, (geometrically?), that using a Raveled Equation for computation would be prohibitive. This deals a fatal blow to the content-based Seed and Root Equation for individual computations. IIB: begins the examination of what the Seed & Root Equations have to tell us about the structure of Data Streams. While Part A, determined the number of elements in Q Unravelings, Part B, Dimensionality, illustrates the geometrical significance of these numbers. It illustrates that each successive Raveling adds another dimension to the construction of the number that names the quantity of elements in Q unravelings.

#### Section II: C & D

Part C, Impact Diagrams, discusses the fact that while the number of elements is increasing that the impact of each element varies amongst them. It is shown that the potential impact of subsequent data on the Decaying Average decreases in spiral fashion because of scaling. Using these square spiral diagrams it is easily seen that Data Density increases with the increase in N, the number of elements, and D, the Decay Factor. This becomes an important consideration in the generation of stable derivatives. Part D, Fractional Dimensions, discusses this perspective from the perspective of a Line being made up of points. We see that as the number of points increases that the bunchy line appears smooth. Again a large N is stressed to better achieve the illusion of Dimensionality from just a bunch of points.

#### Section II: E & F

Part E, Dimensional Equations, shows our directional equations in terms of their dimensional construction. It is seen that Directionals are a product of the war of dimensions. While the zeroth Directional is the data Raveled once, the first Directional is the difference between the linear response and the past spatial response. The 2nd Directional, the acceleration vector, is the difference of two-dimensional differences. Part F, Collapsible Dimensional Numbers, points out that because of the fractal nature of the Directional system, (Directionals are a Fractal Function Set), that any of numbers could be collapsed or expanded in dimensionality being aware that many changes are qualitative not quantitative. For instance, although the zeroth Directional is only a double unraveling, the first Directional is not the 3rd unraveling but is the difference between a double and triple unraveling. Also, although the 1st Directional is a difference between a double and triple unraveling, the 2nd Directional is not a difference between a triple and quadruple unraveling although it has that element in it. A geometrical understanding of the dimensional composition of Raveled numbers provides part of the understanding. A Nice 3D Spiral Cube. From these notions of Spiral Cubes comes an understanding of Potential Impact of Data on the Higher Levels. {We go into a derivation of the Potential Impact of Individual Data Points on Directionals in another Notebook. 13. Potential Impact & Raveled Numbers.}

#### Sections III->VI

In Section III we discuss some very interesting potential impact graphs. The first point that is made is that each graph can be looked at as the Past's influence upon the Present or as the Present's influence on the Future. They are one and the same in this system. After looking at these graphs, we establish a foundation for potential and real impact. We discover in the process why traditional analysis has no need for the concept of potential impact, which has taken so much time and provided so much interest. We then look at the fractalization of time implicit in Decay. Finally we examine the implications of unpredictability. This leads to another type of scientific method when dealing with living, unpredictable phenomenon.